Quantum repeater using three-level atomic states in the presence of dissipation: stability of entanglement

In this paper we want to investigate the possibility of transferring entanglement to two three-level separable atomic states over large distance using the quantum repeater protocol.In detail, our model consists of eight Λ-type three-level atoms where only the pairs (1,2), (3,4), (5,6) and (7,8) are prepared in maximally entangled states.Performing suitable interaction between non-entangled three-level atoms (2,3) and (6,7) in two-mode cavities with photon leakage rates κ, κ ′ in the presence of spontaneous emission leads to producing entanglement between atoms (1,4) and (5,8), separately.Finally, the entanglement between atoms (1,8) is successfully produced by performing interaction between atoms (4,5) while spontaneous emission is considered in a dissipative cavity.In the continuation, the effects of detuning, dissipation and initial interaction time are considered on negativity and success probability of the processes.The maxima of negativity are decreased by increasing the detuning, in most cases.Also, the time evolution of negativity is non-periodic in the presence of dissipation.Increasing the initial interaction time has a constructive effect on negativity in all considered cases.The oscillations of negativity are destroyed as time goes on and the produced entanglement is stabled.The success probability of entangled state of atoms (1,8) is tunable by controlling the detuning and dissipation.We show that via justifying the involved parameters one can arrive at conditions in which the decoherence effects are fully disappeared; as a result an ideal quantum repeater can be achieved while atomic and field dissipations are taken into account.